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Search: id:A099809
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| A099809 |
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Let a,b be prime numbers satisfying the Diophantine equation a^3+b^3=(a+b)*(a^2-a*b+b^2)=c^2. Then the second factor a^2-a*b+b^2 is 3*e^2 for some integer e. This sequence tabulates the 'e' values, sorted by magnitude of c. |
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+0
5
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| 19, 4513, 14689, 32401, 26929, 48019, 44641, 72739, 124099, 179683, 211249, 288979, 395089, 386131, 587233, 905059, 1040419, 1410049, 2237011, 1919779, 2078209, 2220451, 2950963, 2767489, 4919971, 5582449, 5019889, 5255761
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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For each n let a=A099806[n], b=A099807[n], c/12=A098970. Then a^3+b^3=c^2. The left side factors as (a+b)*(a^2-a*b+b^2). The second factor is 3*e^2 for some integer e. The sequence tabluates the 'e' values. These 'e' values all have the form 3*M^4+N^4, for some pair M,N of relatively prime integers of opposite parity. Remember, a and b are prime numbers.
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LINKS
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James Buddenhagen, Two Primes Cubed which Sum to a Square.
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EXAMPLE
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11^3+37^3=228^2, 11^2-11*37+37^2=3*e^2 with e=19, so 19 is in the sequence.
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CROSSREFS
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Cf. A099806, A099807, A098970, A099808.
Sequence in context: A087353 A055415 A125197 this_sequence A145851 A145214 A013724
Adjacent sequences: A099806 A099807 A099808 this_sequence A099810 A099811 A099812
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KEYWORD
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nonn
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AUTHOR
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James Buddenhagen (jbuddenh(AT)gmail.com), Oct 26 2004
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